International Workshop on 'New challenges in Reduced Density Matrix Functional Theory: Symmetries, time-evolution and entanglement'
Adapting tensor network states to the structure of interacting fermionsChristian Krumnow
The direct computation of the ground state of interacting fermionic systems becomes quickly infeasible with increasing system size due to the exponential size of the Hilbert space. Additional structure present in many physical systems needs to be exploited in order to advance and simulate realistic systems. In recent years it was noted that tensor network states (TNS) are able to capture naturally occurring correlations efficiently such that ground states of distinguishable particles can be approximated using the density matrix renormalization group algorithm . Applied to fermionic systems however, TNS capture correlations partially in the wrong picture as individual Slater determinants might not be efficiently representable. We correct this shortcoming by augmenting TNS with additional degrees of freedom  which allow to systematically optimize the single particle basis. By this we are able to construct ground state search and time evolution methods which adapt the single particle basis according to the correlation structure of the problem automatically. Widening the scope, similar ideas of identifying more optimal structures can be exploited in DFT and establish links between TNS and DFT as we will discuss.
 U. Schollwoeck, Ann. Phys. 326 96 (2011)
 C. Krumnow, L. Veis, Ö. Legeza, J. Eisert, Phys. Rev. Lett. 117 210402 (2016)